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Are real numbers closed under subtraction?

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∙ 7y ago

Updated: 10/16/2024

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Q: Are real numbers closed under subtraction?

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Are real numbers closed under addition and subtraction?

Real numbers are closed under addition and subtraction. To get a number outside the real number system you would have to use square root.

Why are the set of real numbers is not commuted under subtraction and addition?

Real numbers are commutative (if that is what the question means) under addition. Subtraction is a binary operation defined so that it is not commutative.

Which set is closed under the operation of subtraction?

The set of integers, rational numbers, real numbers, complex numbers are some of the sets. Also, many of their subsets: for example, all numbers divisible by 3.

What are the different rules in governing operations of real numbers?

The set of real numbers is closed under addition, subtraction, multiplication, and division (except that you cannot divide by zero). By closed, this means that if the two numbers in the operation are both real numbers, the result of the operation will always be a real number. Dividing by zero is undefined (for all practical purposes)

Can the operation subtraction have properties?

Not by itself. A mathematical operation has properties in the context of a set over which it is defined. It is possible to have a set over which properties are not valid.Having said that, the set of rational numbers is closed under subtraction, as is the set of real numbers or complex numbers.Multiplication is distributive over subtraction.

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Related Questions

Which set of numbers is closed under subtraction?

A set of real numbers is closed under subtraction when you take two real numbers and subtract , the answer is always a real number .

Are real numbers closed under addition and subtraction?

Real numbers are closed under addition and subtraction. To get a number outside the real number system you would have to use square root.

Is the set of real numbers closed under addition?

Yes. The set of real numbers is closed under addition, subtraction, multiplication. The set of real numbers without zero is closed under division.

Which sets of numbers are closed under subtraction?

To be closed under an operation, when that operation is applied to two member of a set then the result must also be a member of the set. Thus the sets ℂ (Complex numbers), ℝ (Real Numbers), ℚ (Rational Numbers) and ℤ (integers) are closed under subtraction. ℤ+ (the positive integers), ℤ- (the negative integers) and ℕ (the natural numbers) are not closed under subtraction as subtraction can lead to a result which is not a member of the set.

What are irrational numbers closed under?

Irrational numbers are not closed under any of the fundamental operations. You can always find cases where you add two irrational numbers (for example), and get a rational result. On the other hand, the set of real numbers (which includes both rational and irrational numbers) is closed under addition, subtraction, and multiplication - and if you exclude the zero, under division.

Is the set of integers closed under subtraction?

yes, because an integer is a positive or negative, rational, whole number. when you subject integers, you still get a positive or negative, rational, whole number, which means that under the closure property of real numbers, the set of integers is closed under subtraction.

Why are the set of real numbers is not commuted under subtraction and addition?

Real numbers are commutative (if that is what the question means) under addition. Subtraction is a binary operation defined so that it is not commutative.

Which set is closed under the operation of subtraction?

The set of integers, rational numbers, real numbers, complex numbers are some of the sets. Also, many of their subsets: for example, all numbers divisible by 3.

What are the different rules in governing operations of real numbers?

The set of real numbers is closed under addition, subtraction, multiplication, and division (except that you cannot divide by zero). By closed, this means that if the two numbers in the operation are both real numbers, the result of the operation will always be a real number. Dividing by zero is undefined (for all practical purposes)

Can the operation subtraction have properties?

Not by itself. A mathematical operation has properties in the context of a set over which it is defined. It is possible to have a set over which properties are not valid.Having said that, the set of rational numbers is closed under subtraction, as is the set of real numbers or complex numbers.Multiplication is distributive over subtraction.

Are real numbers closed under addition?

yes because real numbers are any number ever made and they can be closed under addition

Are real numbers closed under division?

no

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